Biomedical engineering tools and multiple patented inventions of bioimpedance spectroscopy have been concerned with the problems of measuring the resistance and reactance of the human body at a multitude of frequencies in order to determine body composition and hydration status. Advancements in mathematical modeling of the human energy metabolism have provided tools to describe the relationship between energy balance, which is the difference of the energy intake and the total energy expenditure, and body composition changes. State space modeling coupled with the use of time variant minimum variance Kalman filtering or prediction has been successfully used in control engineering for over 50 years to observe and control state variables of complex dynamic systems. This technology holds great potential in monitoring difficult to measure daily body composition changes along with other essential components of the human energy metabolism in order to maximize capabilities of controlling them.
Bioimpedance spectroscopy has become a widely used technique in body composition and hydration status analysis in recent decades. The measurement of impedance, which is measuring resistance and reactance at frequencies from 1 to 1000 kHz, is purported to assist in the determination of extracellular and intracellular water mass. According to the Cole model of body impedance as interpreted by Cornish1, a current at low frequency flows through the extracellular water mass while at higher frequencies it flows through both the extracellular and intracellular water mass, allowing for extracellular and total water mass measurements. The Cole model fitted to resistances and reactances of the human subject at various frequencies can be extrapolated to the resistance values at zero and infinite frequencies. Using the resistance values at zero and an extrapolated infinite frequency, Moissl developed equations corrected with body mass index to calculate extracellular and intracellular water mass.2 The problem with Moissl's equations was that they contained errors in the references, which accounted for the errors in the body mass index corrected extracellular and intracellular water mass calculation's accuracy.3 1 Cornish, DOI: 10.1088/0031-9155/38/3/0012 Moissl, DOI: 10.1088/0967-3334/27/9/0123 Id.
The errors in bioimpedance measurements of extracellular and intracellular water have hampered their accuracy and reliability. When using bioimpedance instruments, artefactual errors occur everywhere along the path of the flowing current around the entire electric circuit, which consists of current sources, a human subject, measurement electrodes, cable connections from subject to measuring instrument, and calibration elements. One example of a disadvantage of the prior art is that the errors due to offset voltage and voltage noise at nodal junction points of the circuit elements cannot be determined, analyzed, and mitigated.4 4 U.S. Pat. No. 5,280,429 (1994).
Moreover, at higher frequencies in bioimpedance spectroscopy, unexpected phase shifts in the results occur due to human subject stray capacitance and the instrument introduces distortions in the results due to nonlinearity. Errors due to stray capacitance are unavoidable in practice, uncontrollable to a large degree, and likely to be more pronounced where other devices are also attached to the subject, but they are measurable. An example of a disadvantage of the prior art is that the errors due to stray capacitances and other measuring errors are neither determined, nor analyzed, nor reduced.5 5 Id.
Another problem with the current bioimpedance spectroscopy technology is the variation in measurement results among machines due to the systemic errors introduced by the techniques, the instrumentation used, and other errors. Another example of the disadvantage of the prior art is that no effort was made to measure quality and inform the user about the size of the detectable error during measurement and about the reliability of the measurement results.6 6 Id.
Another problem with bioimpedance measurements could be the placement of the preamplifier and the drivers of the shielded cables far away from the sensing electrodes. The disadvantage of such arrangements is that the magnitude of the interference from outside electromagnetic sources and the capacitive load from the shielded cables could cause suboptimal results. The prior art uses Fast Fourier Transformation, substituting summation for integration and evaluating only two wavelengths.7 These simplifications would be allowed if the analog to digital conversation were accurate, which it is not. 7 Id.
With regard to measuring variable of human energy metabolism, decades of research into the causes of the obesity epidemic and related scientific research for the cause of it led to the creation of mathematical models of obesity. These models were based on the first law of thermodynamics and proffered that imbalance between energy intake and energy expenditure lead to changes in energy storage, primarily in lipids. The effort to quantify changes of the lipid store led Hall to construct mathematical models describing body composition changes matched to group averages.8 However, everyone's metabolism has unique characteristics, and individualized modeling is needed. Further, there is a need for real-time metabolic modeling and tracking. The Hall models9 work off line when all data are available for retrospective analysis. Differential equations with infinitesimal time resolution are used in the Hall models, requiring significant software capacity to solve and knowledge of how the system changes during the 24 hour time period, when neither is needed for real-time use and for measuring changes every 24 hour period. Importantly, the Hall model equations do not succeed in satisfying the constraint of conservation of energy (i.e. the First Law of Thermodynamics), at the end of each day, which is essential for individualized real-time modeling. Further, Hall does not consider the constraint that the model calculated body composition with its daily change together with changes of hydration status have to add up to the measured body weight and its daily change to allow for individualized real-time modeling. 8 Hall, DOI: 10.1152/ajpendo.00523; DOI: 10.1109/MEMB.2009.935465; DOI: 10.1152/aj pendo. 00559.20099 Hall, DOI: 10.1152/ajpendo.00523; DOI: 10.1152/ajpendo.00559.2009
The imprecision of current methods for determining the variable associated with body composition change, energy expenditure, and energy intake have precluded accurate quantification of the energy balance and thus precluded definitive statements regarding the cause of the obesity epidemic. The currently accepted method for tracking calorie intake in scientific studies of energy balance is self-reported calorie intake counting. For example, the daily ingested calories broken down into the three macronutrient groups are needed every day for the calculations in the Hall models. However, self-reported calorie intake counting is fraught with systemic errors.10 10 Hebert, DOI: 10.1016/S1047-2797(01)00297-6
Model calculations of the macronutrient oxidation rate are an essential component of the modeling of the human energy metabolism. Hall created models for the macronutrient oxidation rates.11 However, Hall's equations are ad-hoc and are inherently nonlinear and not suitable for inverse calculations when model input is sought from known model output. 11 Hall, DOI: 10.1152/ajpendo.00523; DOI: 10.1152/ajpendo.00559.2009
The problems of prediction and noise filtering also exist in the dynamic modeling of the metabolism. The estimation or prediction of the state variables of a dynamic system model poses the challenges of ensuring accuracy and stability of estimations. Therefore, there is a need for accurate and simplified tracking of body composition change, energy expenditure, and especially energy intake exists.
With current clinical trial usage of the bioelectrical impedance measurement method, it has become quite apparent that there are several shortcomings in clinical applications of the method. Some of the concerns of clinical applications are summarized in Buchholtz12 et al. Currently, the clinical applicability and the measurement accuracy are limited to the group level only rather than providing accurate values specific to an individual. The various bioelectrical impedance models and reference methods differ widely across studies. The results are confusing for a clinician and they break down in disease states. 12 Buchholtz et al, DOI: 10.1177/0115426504019005433
There is no consensus on which commercially available biomedical impedance instruments are the best and which electrophysiological models best describe the human body in vivo. Some of the shortcomings of the current instrumentation include but are not limited to: lack of quality measurements of the electrode placement and electrical properties of electrodes during measurements, lack of error calculations, no elimination of flawed data, no error calculations for the model fitting, no overall quality measurements regarding results, and no use of statistical improvement of errors when serial measurements are taken from an individual.
Currently, there is no systematic effort to register important but influencing factors on the measurements such as environmental factors including location and room temperature to measure and compensate for local environmental electromagnetic influences. There is no systematic effort to register physiological factors such as accurate body weight, time of the measurement, duration of measurement, skin temperature, recent exercise status, fluid and food consumption diary, timing of last bladder emptying, and bowel movement among others.
The simplistic use of the Cole model is inadequate to capture important changes regarding conductivity and permittivity13 which occur during acute changes of hydration. The impedance models currently in use fail to predict changes of extracellular water and total body water during short term 2-3% dehydration and rehydration.14 The Cole model is not individualizable to suit current demand. 13 Gerritsen et al, DOI:10.1088/1742-6596/434/1/01200514 Asselin et al, DOI: 10.1016/S0969-8043(97)00179-6
The problems of measuring hydration status changes with current bioimpedance methods carry over to the problem of measuring body composition changes. The current methods of measuring body composition changes with the bioimpedance spectroscopy method rely primarily on the determination of extracellular as well intracellular water masses.
Current bioimpedance spectroscopy methods revealed significant systematic errors in the difference between fluid volumes and the reference in the extremes of body mass index.15 These significant systematic errors are due to large variations of the calculated resistances at zero and infinite frequencies, suggestive of the inadequacy of the applied Hanai mixture theory applied together with the Cole model to describe human immittance. 15 Moissl, DOI: 10.1088/0967-3334/27/9/012